With only a few exceptions, the answer to these questions is no.
Déjà Vu X3 can export documents in the same format as the original. Therefore, it can import, e.g., a Word document and export a Word document, but it cannot export an "unclean" version of this document, since that would be a different format.
Similarly, Déjà Vu X3 can import Trados Workbench projects ("unclean" files, in Trados parlance), as well as several other Trados formats, but it will only export a file of the same format as the imported one.
Therefore, if you want to export an "unclean" file from Déjà Vu X3, you must create the unclean file first in Trados, and then import that into Déjà Vu X3. If, on the other hand, you want to export a "clean" file from Déjà Vu X3, you must not import a file that is "unclean".
Exceptions to the rule
As mentioned above, there are a few exceptions to what was explained above, and they all have to do with the creation of External View files by the Workgroup edition of Déjà Vu X3.
Déjà Vu X3 Workgroup can export external view files in various formats, among them Trados RTF (an "unclean" file) and XLIFF (which is not, strictly speaking, "unclean", but can be processed with Trados Studio).
External View files, however, are not really a substitute for an "unclean" file: they cannot be cleaned, at least not in such a way that the original "clean" document will be obtained. They are primarily intended to be used as a method to outsource translation work to translators who are using Trados or other CAT tools different from Déjà Vu X3.